If a,b and c are the greatest values of C_p19,C_q20 and C_r21 respectively, then:

Q48 / 75 · JEE Main 2020 (08 Jan Shift 1) · Mathematics

If $a, b$ and $c$ are the greatest values of ${}^{19}{C_{p}}, {}^{20}{C_{q}}$ and ${}^{21}{C_{r}}$ respectively, then:

We know that, $^{n} C_{r}$ is maximum at middle term.

$a =^{19} C_{p} =^{19} C_{10} =^{19} C_{9}$

$b =^{20} C_{q} =^{20} C_{10}$

$c =^{21} C_{6} =^{21} C_{10} =^{21} C_{11}$

Hence,

$\frac{a}{^{19} C_{9}} = \frac{a}{\frac{20}{10} .^{19} C_{9}} = \frac{a}{\frac{21}{11} . \frac{20}{10} .^{19} C_{9}}$

$\Rightarrow \frac{a}{1} = \frac{b}{2} = \frac{c}{(\frac{42}{11})}$

$\Rightarrow \frac{a}{11} = \frac{b}{22} = \frac{c}{42}$

Hence, the correct answer is option: 'C'.